Orlicz norm inequalities for the composite operator and applications. (English) Zbl 1275.26023

Summary: We first prove Orlicz norm inequalities for the composition of the homotopy operator and the projection operator acting on solutions of the nonhomogeneous A-harmonic equation. Then we develop these estimates to \(L^\phi(\mu)\)-averaging domains. Finally, we give some specific examples of Young functions and apply them to the norm inequality for the composite operator.


26B10 Implicit function theorems, Jacobians, transformations with several variables
26D20 Other analytical inequalities
30C65 Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Full Text: DOI


[1] doi:10.1006/jmaa.2000.6850 · Zbl 0973.35074
[2] doi:10.1088/0951-7715/23/5/005 · Zbl 1190.35090
[3] doi:10.1016/j.camwa.2004.06.016 · Zbl 1063.30022
[4] doi:10.1016/S0022-247X(03)00216-6 · Zbl 1027.30053
[5] doi:10.1016/j.aml.2009.01.041 · Zbl 1173.58300
[6] doi:10.1007/BF00411477 · Zbl 0793.58002
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